16 Nov 2020

Publication Notification: Distribution of the Two-Point Product of Complex Amplitudes in the Fully Saturated Scattering Regime

Abstract:  This Letter considers probability density functions (pdfs) involving products of the complex amplitudes observed at two points (which may, in general, involve separations in space, time, or frequency) in conditions of fully saturated scattering. First, the pdf is derived for the product of the complex amplitude at one point with the conjugate of the complex amplitude at another point. It is shown that the real and imaginary parts of this product each have a variance gamma pdf. Second, expressions are derived for several joint pdfs involving complex amplitude products and powers at two points.

5 Nov 2020

A Measurement System for the Study of Nonlinear Propagation Through Arrays of Scatterers

Abstract: Various experimental challenges exist in measuring the spatial and temporal field of a nonlinear acoustic pulse propagating through an array of scatterers. Probe interference and undesirable high-frequency response plague typical approaches with acoustic microphones, which are also limited to resolving the pressure field at a single position. Measurements made with optical methods do not have such drawbacks, and schlieren measurements are particularly well suited to measuring both the spatial and temporal evolution of nonlinear pulse propagation in an array of scatterers. Herein, a measurement system is described based on a z-type schlieren setup, which is suitable for measuring axisymmetric phenomena and visualizing weak shock propagation. In order to reduce directivity and initiate nearly spherically-symmetric propagation, laser induced breakdown serves as the source for the nonlinear pulse. A key component of the schlieren system is a standard schliere, which allows quantitative schlieren measurements to be performed. Sizing of the standard schliere is aided by generating estimates of the expected light refraction from the nonlinear pulse, by way of the forward Abel transform. Finally, considerations for experimental sequencing, image capture, and a reconfigurable rod array designed to minimize spurious wave interactions are specified.